The Research Of Black-Scholes Model

Option is the core tool to risk management. Option theory is one of the greatest findings in the area of the world's economics in the 20th century. Scholes and Merton(Black)who had gained the Nobel Prize made greatly dedication to the theory of option prcing. The research on option pricing theory is focused on the following two aspects: one is how to design new options to satisfy the changing investment demand; the other is how to price the more and more complicated options,i.e. option pricing.To solve the B-S's pricing formulas,there are many popular methods now,such as partial differential equation,analytical approximation,binomial tree methods,finite difference method and Monte-Carlo simulation.We systematically represent a new mean of solving the model—the method of integral transformation by the theory of integral transformation in this paper. And we research the model in the aspect of quantity and quality. Specially, we primary deals with the option pricing of Black-Scholes model with continuous dividend payments then get the call option and put option formulas: And the model of geometric average Asian options with fixed strike price then we get the call option formula: The relevant formulas about call option and put option,which are all identical with the classical ones.